Exercise 12 Page 265

Rewrite the terms so that they have a common base.

x=-3/2

Practice makes perfect

To solve the given exponential equation, we will start by rewriting the terms so that they have a common base.

16^x = 1/64

WritePow

Write as a power

(4^2)^x = 1/4^3

FracToNegExponent

1/a^m=a^(- m)

(4^2)^x = 4^(-3)

PowPow

(a^m)^n=a^(m* n)

4^(2x)=4^(-3)

Now, we have two equivalent expressions with the same base. If both sides of the equation are equal, the exponents must also be equal. 4^(2x)=4^(-3) ⇔ 2x = -3 Finally, we will solve the equation 2x = -3.

2x = -3

DivEqn

.LHS /2.=.RHS /2.

x = - 3/2

Subchapter links

1 Graphing Exponential Functions p.265

2 Solving Exponential Equations and Inequalities p.265

3 Simplifying Radical Expressions p.265

4 Operations with Radical Expressions p.266

5 Radical Equations p.266

Exercise 12 Page 265

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